Time-Delay Synchronization and Anti-Synchronization of Variable-Order Fractional Discrete-Time Chen–Rossler Chaotic Systems Using Variable-Order Fractional Discrete-Time PID Control

Joel Perez Padron, Jose Paz Perez, José Javier Pérez Díaz and Atilano Martinez Huerta
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Joel Perez Padron: The Dynamical Systems Group, Department of Physical and Mathematical Sciences, Universidad Autónoma de Nuevo León, San Nicolás de los Garza 66451, NL, Mexico
Jose Paz Perez: The Dynamical Systems Group, Department of Physical and Mathematical Sciences, Universidad Autónoma de Nuevo León, San Nicolás de los Garza 66451, NL, Mexico
José Javier Pérez Díaz: Department of Mechanical and Electrical Engineering, Universidad Autónoma de Nuevo León, San Nicolás de los Garza 66451, NL, Mexico
Atilano Martinez Huerta: The Dynamical Systems Group, Department of Physical and Mathematical Sciences, Universidad Autónoma de Nuevo León, San Nicolás de los Garza 66451, NL, Mexico

Mathematics, 2021, vol. 9, issue 17, 1-15

Abstract: In this research paper, we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional-order differential equations. To guarantee the synchronization and anti-synchronization, we use the well-known PID (Proportional-Integral-Derivative) control theory and the Lyapunov–Krasovskii stability theory for discrete systems of a variable fractional order. We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of a variable fractional order with discrete time delay.

Keywords: variable-order fractional-discrete time systems; synchronization and anti-synchronization; Lyapunov–Krasovskii stability; fractional-order Caputo derivative; time-delay fractional-discrete systems; fractional-order discrete time PID control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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